Question

A conducting rod of length l, rotates about one of its ends in a uniform magnetic field B, with a constant angular velocity ω. If the plane of rotation is perpendicular to B, the e.m.f. induced between the ends of rod is ______.

Options

• `1/2 B omega l^2`

• Bωl²

• 2Bωl²

• Bωl

Answer 1

A conducting rod of length l, rotates about one of its ends in a uniform magnetic field B, with a constant angular velocity ω. If the plane of rotation is perpendicular to B, the e.m.f. induced between the ends of rod is `bbunderline(1/2 B omega l^2)`.

Explanation:

When the rod rotates in a magnetic field perpendicular to the plane of rotation, each small element produces a small induced e.m.f. On integrating along the length of the rod from 0 to l, the total induced e.m.f. is:

E = `1/2 B omega l^2`